Skip to main content
SpringerLink
Log in

The Physical Fundamentals of the Ultrasonic Nondestructive Stress Analysis of Solids

  • Published:
International Applied Mechanics Aims and scope

Abstract

Theoretical and experimental works on acoustoelasticity are briefly generalized. Studies conducted and scientific results obtained at the S. P. Timoshenko Institute of Mechanics and E. O. Paton Institute of Electric Welding of the National Academy of Sciences of Ukraine are highlighted. Special features of these works and their difference from those of other authors are pointed out. The basic principles and laws governing the propagation of longitudinal, shear, and surface waves in bi- and triaxially stressed bodies are briefly stated with regard for the orthotropy and nonlinear properties of the material. The experimentally proven principles and laws for elastic waves propagating in initially stressed bodies are formulated. The physical fundamentals of the ultrasonic nondestructive technique for determining bi- and triaxial stresses in solids are described. The determination of bi- and triaxial residual stresses in specimens and structural members is demonstrated by examples. The basic principles of the related (dielectric and electromagnetic) methods for stress analysis of polymeric materials are stated. The application of the electromagnetic method to the stress analysis of some polymeric materials is considered

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. S. Yu. Babich, A. N. Guz', and A. P. Zhuk, “Elastic waves in bodies with initial stresses,” Prikl. Mekh., 15, No. 4, 3–23 (1979).

    Google Scholar 

  2. V. M. Bobrenko, M. S. Vangeli, and A. N. Kutsenko, Acoustic Stress Analyses of Machine Parts [in Russian], Shtiintsa, Kishinev (1981).

    Google Scholar 

  3. V. M. Bobrenko and Ya. A. Rublev, “Rayleigh waves in the quality evaluation of surface cold working,” Defektoskopiya, No. 5, 18–22 (1976).

    Google Scholar 

  4. M. Born and E. Wolf, Principles of Optics [Russian translation], Nauka, Moscow (1970).

    Google Scholar 

  5. G. A. Budenkov and Zh. G. Nikiforenko, “Using ultrasound to determine the internal elastic anisotropy of materials,” Defektoskopiya, No. 3, 18–21 (1967).

    Google Scholar 

  6. G. A. Budenkov, Zh. G. Nikiforenko, and I. É. Shkol'nik, “Ultrasonic stress analysis of materials,” Zavod. Labor., 12, No. 6, 962–965 (1966).

    Google Scholar 

  7. I. P. Vasil'chenko and B. L. Pelekh, Fundamentals of the Electromagnetic Method for Stress Analysis of Anisotropic Media [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  8. F. F. Voronov and L. F. Vereshchagin, “The effect of hydrostatic pressure on the elastic properties of materials,” FMM, 2, No. 3, 443–450 (1961).

    Google Scholar 

  9. A. N. Guz', Generality, Vol. 1 of the two-volume series Elastic Waves in Initially Stressed Bodies [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  10. A. N. Guz', Propagation Laws, Vol. 2 of the two-volume series Elastic Waves in Initially Stressed Bodies [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  11. A. N. Guz', “Elastic waves in initially stressed compressible materials and a nondestructive ultrasonic method for determination of biaxial residual stresses,” Prikl. Mekh., 30, No. 1, 3–17 (1994).

    Google Scholar 

  12. A. N. Guz', O. I. Gushcha, F. G. Makhort, and V. K. Lebedev, “Application of acoustoelasticity to the measurement of stresses in deformable bodies,” in: Proc. 9th All-Union Acoust. Conf., Sec. 6, Moscow (1977), pp. 123–126.

  13. A. N. Guz’ and F. G. Makhort, “Description of the effect of finite strains on the velocity of elastic waves,” Dokl. Akad. Nauk SSSR, 198, No. 2, 316–318 (1971).

    Google Scholar 

  14. A. N. Guz’ and F. G. Makhort, “Substantiation of the theory of stress analysis using electromagnetic waves,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 896–899 (1978).

    Google Scholar 

  15. A. N. Guz’ (general editor) and F. G. Makhort, Acoustoelectromagnetoelasticity, Vol. 3 of the five-volume series The Mechanics of Coupled Fields in Structural Elements [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  16. A. N. Guz', F. G. Makhort, and O. I. Gushcha, An Introduction to Acoustoelasticity [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  17. A. N. Guz', F. G. Makhort, O. I. Gushcha, and V. K. Lebedev, “The theory of wave propagation in an elastic isotropic body with initial strains,” Prikl. Mekh., 6, No. 12, 42–49 (1970).

    Google Scholar 

  18. A. N. Guz', F. G. Makhort, O. I. Gushcha, and V. K. Lebedev, “The theory of ultrasonic initial-stress analysis,” Prikl. Mekh., 7, No. 6, 110–113 (1971).

    Google Scholar 

  19. A. N. Guz', F. G. Makhort, O. I. Gushcha, and V. K. Lebedev, Fundamentals of the Ultrasonic Nondestructive Stress-Analysis Technique for Solids [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  20. A. N. Guz', F. G. Makhort, G. G. Margolin, and A. L. Bogaichuk, “The effect of elastic strains on the permittivity of composites,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 45–49 (1981).

    Google Scholar 

  21. O. I. Gushcha, A. N. Guz', F. G. Makhort, and V. K. Lebedev, “Increasing the accuracy of the acoustic stress-analysis technique,” Probl. Prochn., No. 1, 114–116 (1977).

    Google Scholar 

  22. O. I. Gushcha and V. K. Lebedev, “Ultrasonic measurements of stresses in metals,” in: Ultrasound in the Chemical and Machine-Building Industry [in Russian], Izd. KDNTI, Kiev (1967), pp. 89–92.

    Google Scholar 

  23. O. I. Gushcha and V. K. Lebedev, “Improvement of the pulse ultrasonic-velocity measurement method,” Zavod. Labor., No. 7, 833–835 (1967).

    Google Scholar 

  24. O. I. Gushcha, V. K. Lebedev, A. N. Guz', and F. G. Makhort, “Some results of application of the ultrasonic nondestructive technique to the determination of residual stresses,” Probl. Prochn., No. 8, 71–78 (1973).

    Google Scholar 

  25. O. I. Gushcha and F. G. Makhort, “An acoustic method for determination of biaxial residual stresses,” Prikl. Mekh., 12, No. 10, 32–36 (1976).

    Google Scholar 

  26. O. I. Gushcha and F. G. Makhort, “Wave-propagation nonlinearity in initially stressed solids,” Prikl. Mekh., 22, No. 1, 7–12 (1986).

    Google Scholar 

  27. O. I. Gushcha and F. G. Makhort, “Application of the acoustic method to the determination of residual stresses in welded structures,” Tekhn. Diagn. Nerazrush. Kontr., No. 4, 8–15 (1995).

    Google Scholar 

  28. V. A. Znova, F. G. Makhort, and O. I. Gushcha, “Ultrasonic stress analysis of initially stressed bodies,” Prikl. Mekh., 22, No. 10, 67–72 (1986).

    Google Scholar 

  29. F. G. Makhort, “The theory of propagation of surface waves in an initially strained elastic body,” Prikl. Mekh., 7, No. 2, 34–40 (1971).

    Google Scholar 

  30. F. G. Makhort, “Some acoustic relations of Rayleigh waves for stress analysis of deformable bodies,” Prikl. Mekh., 14, No. 10, 123–125 (1978).

    Google Scholar 

  31. F. G. Makhort, “Substantiation of the theory of stress analysis using electromagnetic waves,” Prikl. Mekh., 15, No. 3, 17–23 (1979).

    Google Scholar 

  32. F. G. Makhort and O. I. Gushcha, “Fundamentals of the theory of ultrasonic triaxial-stress analysis,” Prikl. Mekh., 23, No. 1, 18–23 (1987).

    Google Scholar 

  33. F. G. Makhort, O. I. Gushcha, and A. A. Chernoochenko, “The effect of static stresses on the properties and behavior of surface acoustic waves,” in: Diagnostics and Failure Prediction of Welded Structures [in Russian], Issue 6 (1988), pp. 25–30.

    Google Scholar 

  34. F. G. Makhort, O. I. Gushcha, and A. A. Chernoochenko, “The theory of acoustoelasticity of surface Rayleigh waves,” Prikl. Mekh., 26, No. 4, 35–41 (1990).

    Google Scholar 

  35. F. G. Makhort, O. I. Gushcha, and A. A. Chernoochenko, “On some laws of propagation of Rayleigh waves in bodies with initial stresses,” Prikl. Mekh., 29, No. 11, 47–52 (1993).

    Google Scholar 

  36. F. G. Makhort, O. I. Gushcha, and A. A. Chernoochenko, “The nonlinear properties of solids and some features of propagation of Rayleigh waves in bodies with initial stresses,” Prikl. Mekh., 31, No. 2, 62–66 (1995).

    Google Scholar 

  37. F. G. Makhort and V. A. Znova, “Development of the ultrasonic method for determination of residual stresses in initially anisotropic bodies,” Prikl. Mekh., 23, No. 12, 55–60 (1987).

    Google Scholar 

  38. A. N. Guz’ (general editor), The Mechanics of Composites and Structural Elements (Vol. 3, Applied Research) [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  39. A. N. Guz’ (ed.), Nondestructive Testing of Materials and Structural Elements [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  40. B. E. Paton, V. I. Trufyakov, O. I. Gushcha, A. N. Guz', and F. G. Makhort, “The ultrasonic nondestructive technique for measurement of stresses in welded structures,” in: Diagnostics and Failure Prediction of Welded Structures [in Russian], Issue 2 (1986), pp. 13–19.

    Google Scholar 

  41. G. N. Savin, A. A. Lukashov, E. M. Lysko et al., “Propagation of elastic waves in a nonlinearly elastic solid,” Prikl. Mekh., 6, No. 2, 38–42 (1970).

    Google Scholar 

  42. S. S. Sekoyan, “Calculation of the elastic constants of the third order from results of ultrasonic measurements,” Akust. Zh., 16, No. 3, 453–457 (1970).

    Google Scholar 

  43. S. S. Sekoyan, “Study of the effect of static stresses on the velocity of elastic waves in steel and determination of elastic moduli of the third order,” in: Elasticity and Inelasticity [in Russian], Issue 1, Moscow (1971), pp. 268–269.

    Google Scholar 

  44. S. S. Sekoyan and A. E. Eremeev, “Ultrasonic measurement of the elastic constants of the third order for steel,” Izmer. Tekhn., No.7, 25–30 (1966).

    Google Scholar 

  45. S. S. Sekoyan and A. E. Eremeev, “Measurement of the Murnaghan constant n for steel using the method of elliptically polarized waves,” Izmer. Tekhn., No. 10, 20–24 (1966).

    Google Scholar 

  46. S. S. Sekoyan and E. K. Subbotina, “Propagation of elastic waves in an infinite body with initial stresses,” Prikl. Mekh., 8, No. 2, 113–115 (1972).

    Google Scholar 

  47. T. R. Tiersten, “Wave propagation in fluids and solids,” in: Methods and Devices, Vol. 1, Part A of the series W. P. Marson (ed.), Physical Acoustic. Principles and Methods, Acad. Press, New York-London (1964).

    Google Scholar 

  48. M. M. Frocht, Photoelasticity [Russian translation], Vol. 1, OGIV, Moscow-Leningrad (1948).

    Google Scholar 

  49. M. Hayes and R. S. Rivlin, “Propagation of a plane wave in an isotropic elastic material subjected to pure homogeneous deformation,” Arch. Ratl. Mech. Anal., 8, No. 1, 15–22 (1961).

    Google Scholar 

  50. A. A. Chernoochenko, F. G. Makhort, and O. I. Gushcha, “Application of the acoustoelastic theory of surface Rayleigh waves to the stress analysis of solids,” Prikl. Mekh., 27, No. 1, 44–49 (1991).

    Google Scholar 

  51. A. A. Chernoochenko, F. G. Makhort, and O. I. Gushcha, “Application of Rayleigh waves in studying the nonlinear elastic properties of near-surface layers of structural materials,” Prikl. Mekh., 28, No. 7, 33–37 (1992).

    Google Scholar 

  52. T. B. Bateman, W. R. Mason, and H. J. McSkimin, “Third-order elastic moduli of Germanium,” J. Appl. Phys., 32, No. 5, 928–936 (1961).

    Google Scholar 

  53. R. W. Benson and V. J. Raelson, “From ultrasonics a new stress-analysis technique. Acoustoelasticity,” Prog. Engng., 30, 56–59 (1959).

    Google Scholar 

  54. R. N. Bergman and R. A. Shahbender, “Effect of statically applied stresses on the velocity of propagation of ultrasonic waves,” J. Appl. Phys., 29, No. 12, 1736–1739 (1958).

    Google Scholar 

  55. E. H. Bocardus, “Third-order elastic constants of Ge, MgO, and fused SiO2,” J. Appl. Phys., 36, No. 8, 2504–2513 (1965).

    Google Scholar 

  56. K. Brugger, “Thermodynamic definition of higher order elastic coefficients,” Phys. Rev., 133, No. 6A, 1611–1612 (1964).

    Google Scholar 

  57. D. I. Crecraft, “The measurement of applied and residual stresses in metals using ultrasonic waves,” J. Sound Vib., 5, 173–192 (1967).

    Google Scholar 

  58. D. I. Crecraft, “Ultrasonic wave velocities in stressed nickel steel,” Nature, 195, No. 487, 193–194 (1962).

    Google Scholar 

  59. J. N. Flavin and A. E. Green, “Plane thermoelastic wave in an initially stressed medium,” J. Mech. Phys. Solids, 9, No. 3, 179–190 (1961).

    Google Scholar 

  60. H. Fokuoka, H. Toda, and Yamanet, “Acoustoelastic stress analysis of residual stresses in a patch welded disk,” Exp. Mech., 18, 277–280 (1978).

    Google Scholar 

  61. J. R. Frederick, “Use of ultrasonic surface waves in the determination of residual stress in metals,” J. Acoust. Soc. Am., 32, 1499 (1980).

    Google Scholar 

  62. V. T. Golovchan, “Elastic moduli of a tungsten monocarbide crystal,” Int. Appl. Mech., 34, No. 8, 755–757 (1998).

    Google Scholar 

  63. A. E. Green, “Thermoelastic stresses in initially stressed bodies,” Proc. Roy. Soc., 266, No. 1324, 1–19 (1962).

    Google Scholar 

  64. A. E. Green, “A note on wave propagation in initially deformed bodies,” J. Mech. Phys. Solids, 14, No. 2, 119–126 (1963).

    Google Scholar 

  65. A. E. Green, “Ultrasonic investigation of mechanical properties,” in: Treatise on Materials Science and Technology, Vol. 3, Academic Press, New York (1973).

    Google Scholar 

  66. A. N. Guz', “On deformational anisotropy,” in: Colloques Internationaux du CNRS, No. 295, Comportement Mecanicus des Solides Anisotropes (1982), pp. 675–684.

  67. A. N. Guz', “Nondestructive ultrasound method of determination of biaxial stresses,” Proc. 9th Int. Conf. on Experimental Mechanics Baby Tryk, Copenhagen, Denmark, Vol. 3 (1990), pp. 1171–1179.

    Google Scholar 

  68. A. N. Guz', “Elastic waves in compressible materials with initial stresses and nondestructive ultrasonic method of determination of two-axial residual stresses,” in: Abstracts of Papers Read at 18th Int. Congr. on Theoretical and Applied Mechanics (Haifa, Israel, August 22–28) (1992).

  69. A. N. Guz', “Elastic waves and nondestructive ultrasonic method of determination of two-axial stresses,” in: Proc. 10th Int. Conf. Experimental Mechanics (July 18–22, 1994, Lisbon, “Recent Advances in Experimental Mechanics”), A. A. Balkemy, Netherland (1994), pp. 723–728.

    Google Scholar 

  70. A. N. Guz', “Surface waves in bodies with initial stresses and ultrasonic nondestructive method of determination of stresses in near-the-surface layers of bodies,” in: Abstracts of Papers Read at 19th Int. Congr. Theoretical and Applied Mechanics (Kyoto, Japan, August 25–31) (1996).

  71. A. N. Guz', “Surface waves in bodies with initial stresses and an ultrasonic nondestructive method for determining stresses in near-surface layers of solids,” Int. Appl. Mech., 34, No. 4, 315–327 (1998).

    Google Scholar 

  72. M. Hayes, “Wave propagation and uniqueness in prestressed elastic solids,” Proc. Roy. Soc., A274, No. 1359, 500–506 (1963).

    Google Scholar 

  73. M. Hayes, “A remark on Hadamard materials,” Quart. J. Mech. Appl. Math., 21, No. 2, 141–146 (1968).

    Google Scholar 

  74. M. Hayes and R. S. Rivlin, “Surface waves in deformed elastic materials,” Arch. Rat. Mech. Anal., 8, No. 1, 358–380 (1961).

    Google Scholar 

  75. N. N. Hsu, “Acoustoelastic birefringence in the use of ultrasonic waves for experimental stress analysis,” Exp. Mech., 14, 169–176 (1974).

    Google Scholar 

  76. D. S. Hugnes and J. L. Kelly, “Second-order elastic deformation of solids,” Phys. Rev., 92, No. 5, 1145–1149 (1953).

    Google Scholar 

  77. D. Husson, S. D. Bannett, and G. S. Kino, “Measurement of surface stresses using Rayleigh waves,” in: Proc. Ultrason. Symp. (San Diego, California, October 27–29, 1982), Vol. 2, New York (1982), 889–892.

    Google Scholar 

  78. D. Husson, S. D. Bannett, and G. S. Kino, “Rayleigh wave measurement of surface residual stresses,” in: Proc. 10th Ann. Rev. Progr. Quant. Nondestruct. Eval. (Santa Cruz, California, August 7–12, 1983), Vol. 38, New York-London (1984), pp. 1293–1303.

    Google Scholar 

  79. D. Husson, S. D. Bannett, and G. S. Kino, “Measurement of stress with surface waves,” Mat. Eval., 43, No. 1, 92–100 (1985).

    Google Scholar 

  80. K. Jassby and D. Rishoni, “Experimental technique for measurement of stress-acoustic coefficients of Rayleigh waves,” Exp. Mech., 23, No. 1, 74–80 (1983).

    Google Scholar 

  81. G. S. Kino, J. B. Hunter, G. C. Johnson, A. R. Selfringe, D. M. Barnett, Hermann, and C. R. Steele, “Acoustoelastic imaging of stress field,” J. Appl. Phys., 50, 2607–2613 (1979).

    Google Scholar 

  82. B. G. Martin, “Rayleigh wave-velocity, stress, and preferred grain orientation in aluminum,” Nondestruct. Test. Research Practice, 7, 199–201 (1974).

    Google Scholar 

  83. B. G. Martin, “The measurement of surface and near-surface stress in aluminum alloy using ultrasonic Rayleigh waves,” Mater. Eval., 32, No. 11, 229–234 (1974).

    Google Scholar 

  84. G. T. Mase, “Rayleigh wave speeds in transversely isotropic materials,” J. Acoust. Soc. Am., 81, No. 5, 1441–1445 (1987).

    Google Scholar 

  85. G. T. Mase and G. C. Johnoson, “An acoustoelastic theory for surface waves in anisotropic media,” ASME J. Appl. Mech., 54, 127–130 (1987).

    Google Scholar 

  86. A. H. Meitzler and A. H. Fitch, “Acoustoelastic effect in vitreous silica, Pyrex, and T-40 glass,” J. Appl. Phys., 40, No. 4, 1614–1621 (1969).

    Google Scholar 

  87. F. D. Murnaghan, Finite Deformation of an Elastic Solid, Willey and Sons, New York (1951).

    Google Scholar 

  88. R. W. Ogden, “Waves in isotropic elastic materials of Hadamard, Green, and harmonic type,” J. Mech. Phys. Solids, 18, No. 2, 149–163 (1970).

    Google Scholar 

  89. Y. H. Pao, W. Suche, and H. Fokuoka, “Acousto-elasticity and ultrasonic measurements of residual stresses,” in: Phys. Acoust., Vol. 17, (W. P. Mason and R. N. Thurston (eds.), Principles and Methods), Acad. Press, New York (1984), pp. 61–143.

    Google Scholar 

  90. Ya. Ya. Rushchitskii, “On classification of elastic waves,” Int. Appl. Mech., 35, No. 11, 1104–1110 (1999).

    Google Scholar 

  91. C. O. Ruud, “A review of selected non-destructive methods for residual stress measurement,” NDT Int., No. 1 (1982).

  92. A. Seeger and O. Buck, “Die experiment ermittung der elastischen Konstanten hoherer ordnung,” Z. Naturforsch, 15A, No. 12, 1056–1060 (1960).

    Google Scholar 

  93. R. T. Smith, “Stress induced anisotropy in solids. The acoustoelastic effect,” Ultrasonics, 1, No. 3, 135–147 (1965).

    Google Scholar 

  94. R. T. Smith, R. Stern, and R. W. Stephens, “Third-order elastic moduli of polycrystalline metals from ultrasonic velocity measurements,” J. Acoust. Soc. Am., 40, No. 5, 1002–1008 (1966).

    Google Scholar 

  95. R. N. Thurston and K. Brugger, “Third-order elastic constants and the velocity of small amplitude elastic wave in homogeneously stressed medial,” Phys. Rev., 153, No. 6A, 1604–1610 (1964).

    Google Scholar 

  96. M. E. Todoro and G. P. Capsimalis, “Acousto-elastic effect for Rayleigh surface waves in the present of nonuniform stress field,” in: Proc. IEEE Ultrason. Symp. (Williamsburg, Va, November 17–19, 1986), Vol. 1, New York (1986), pp. 229–232.

    Google Scholar 

  97. T. Tokuoka and Yu. Iwashimizu, “Acoustical birefringence of ultrasonics waves in deformed isotropic elastic materials,” Int. J. Solids Struct., 4, No. 3, 383–389 (1968).

    Google Scholar 

  98. T. Tokuoka and M. Saito, “Elastic wave propagation and acoustical birefringence in stressed crystals,” J. Acoust. Soc. Am., 45, No. 5, 1241–1246 (1969).

    Google Scholar 

  99. R. A. Toupin and B. Bernstein, “Sound waves in deformed perfectly elastic materials. Acoustoelastic effect,” J. Acoust. Soc. Am., 33, No. 2, 216–225 (1961).

    Google Scholar 

  100. R. C. Tripothi and G. S. Verma, “Third-order elastic constants of Ge at room and liquid-nitrogen temperatures,” J. Appl. Phys., 41, No. 7, 2999–3002 (1970).

    Google Scholar 

  101. C. Truesdell, “General and exact theory of waves in finite elastic strain,” Arch. Rat. Mech. Anal., 8, No. 4, 263–296 (1961).

    Google Scholar 

  102. A. Tverdokhlebov, “On the acoustoelastic effect,” J. Acoust. Soc. Am., 73, No. 6, 2006–2012 (1983).

    Google Scholar 

  103. V. V. Zozulya and N. V. Fenchenko, “Influence of contact interaction between the sides of crack on characteristics of failure mechanics in action of P- and SV-waves,” Int. Appl. Mech., 35, No. 2, 175–180 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    A. N. Guz' & F. G. Makhort

Authors
  1. A. N. Guz'
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. G. Makhort
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guz', A.N., Makhort, F.G. The Physical Fundamentals of the Ultrasonic Nondestructive Stress Analysis of Solids. International Applied Mechanics 36, 1119–1149 (2000). https://doi.org/10.1023/A:1009442132064

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009442132064

Keywords

Search

Navigation